A method for the prediction of future values of \(\alpha \) -stable, power GARCH models using auxiliary processes (exogenous predictor) is presented. This predictor is optimal in the sense of minimization of the conditional mean square error. Simulation studies demonstrate that, compared to a standard (endogenous) prediction method, this \(\alpha \) -stable GARCH predictor is capable of reducing the relative mean absolute error by 1% to 20%, depending on the spectral measure and value of the tail index. Empirical examples computed from financial time series for real stocks, showed time averaged reduction in mean absolute errors of 17% to 24%. Comparison of the new method against predictions from feed-forward neural networks showed nearly the same level of accuracy.
